Have you tried the 59cm? It might be worth it as the 61 is only 1cm longer so providing the drops not too severe it could fit you with the right stem. What's the top tube length on your Dawes? I'm imagine the Bianchi has a steeper seatube angle too, which effectively makes it longer.
Obviously you want a perfect fit but imo it's worth trying, as the more bikes you try the more you get to know exactly what you want.
Having said that it may be way too small, I have no idea of rough height-bike size at that end of the spectrum as I ride a 52cm!
PS: I feel your pain. I have an irrational desire for a Bianchi. Ordered one in to try but they screwed me around so much I ended up going somewhere else and getting a Scott instead. It's not as beautiful but it rides well and I'm really happy with it. I will have a Bianchi one day though